Solve for $x$ and $y$ using elimination. ${-2x+6y = 42}$ ${2x-5y = -34}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-2x+6y = 42}\thinspace$ to find $x$ ${-2x + 6}{(8)}{= 42}$ $-2x+48 = 42$ $-2x+48{-48} = 42{-48}$ $-2x = -6$ $\dfrac{-2x}{{-2}} = \dfrac{-6}{{-2}}$ ${x = 3}$ You can also plug ${y = 8}$ into $\thinspace {2x-5y = -34}\thinspace$ and get the same answer for $x$ : ${2x - 5}{(8)}{= -34}$ ${x = 3}$